Optical apparatus with structure for liquid invariant performance

ABSTRACT

A phase-adjusting element configured to provide substantially liquid-invariant extended depth of field for an associated optical lens. One example of a lens incorporating the phase-adjusting element includes the lens having surface with a modulated relief defining a plurality of regions including a first region and a second region, the first region having a depth relative to the second region, and a plurality of nanostructures formed in the first region. The depth of the first region and a spacing between adjacent nanostructures of the plurality of nanostructures is selected to provide a selected average index of refraction of the first region, and the spacing between adjacent nanostructures of the plurality of nanostructures is sufficiently small that the first region does not substantially diffract visible light.

FIELD AND BACKGROUND

The present invention relates generally optical systems and apparatus,in particular, to optical lenses having extended depth of field.

Several approaches have been developed for obtaining extended depth offield of an optical apparatus. Recent technologies involving extendeddepth of field for various optical applications, including ophthalmicapplications, are using annular grooves across a standard lens to createa phase retardation that leads to an interference pattern along thefocal distance which, when controlled properly, can provide an extendeddepth of field. An example of this approach is described in U.S. Pat.No. 7,365,917, which is incorporated herein by reference in itsentirety. Other techniques for extending the depth of field includepresenting diffractional optic elements that can diffract the opticalsignal into different diffraction orders thereby realizing a bi-focal ormulti-focal lens that allows a clear vision for different objectdistances using a single passive lens. Both technologies implement phasereshaping by introducing a lateral (i.e., along the surface of the lens)geometrical lens reshaping that produces the required phase retardationalong a few microns in the longitudinal axis of the lens.

GENERAL DESCRIPTION

Aspects and embodiments are directed to a phase-adjusting elementconfigured to provide extended depth of field for an associated opticallens in an environment where liquid may be present. In particular,aspects and embodiments are directed to a phase-adjusting element thatoperates in essentially the same manner despite the presence of liquidin the surrounding environment, and/or is configured to account for thepresence of liquid, and which therefore may provide a substantiallyliquid-invariant extended depth of field for the associated opticallens, as discussed further below.

According to one embodiment, a lens comprises a surface having amodulated relief comprising a first region and a second region, thefirst region having a predetermined depth relative to the second region,and a plurality of nanostructures formed in the first region, andwherein the spacing between adjacent nanostructures of the plurality ofnanostructures is sufficiently small such that the first region does notsubstantially diffract visible light. In one example, the depth of thefirst region and a spacing between adjacent nanostructures of theplurality of nanostructures is selected to provide a predeterminedaverage index of refraction of the first region.

In one example of the lens, the plurality of nanostructures extend awayfrom a base of the first region. In one example, the spacing betweenadjacent nanostructures of the plurality of nanostructures is less thanapproximately a shortest wavelength of visible light in free space. Inanother example, the spacing between adjacent nanostructures of theplurality of nanostructures is less than approximately 400 nanometers.Each nanostructure of the plurality of nanostructures may have a heightthat is less than or equal to the depth of the first region. The firstregion may include, for example, a circular region, an annular region,or a plurality of concentric regions. In one example, the nanostructuresare uniformly spaced apart from one another. In another example, thespacing between the adjacent nanostructures decreases from a largestspacing at a center of the first region to smallest spacing at edges ofthe first region. In another example, the spacing between the adjacentnanostructures is sufficiently small to prevent water from penetratingbetween the nanostructures at atmospheric pressure. The lens may be, forexample, an ophthalmic contact lens, an intraocular lens, a spectaclelens, or any of numerous other types of optical lenses.

According to another embodiment, a lens having a depth of fieldcomprises a phase-adjusting region formed in a lens surface of the lens,the phase-adjusting region extending into the lens by a depth andconfigured to extend the depth of field of the lens, and a plurality ofnanostructures formed in the phase-adjusting region, the plurality ofnanostructures extending away from a base of the phase-adjusting region,wherein a spacing between adjacent nanostructures of the plurality ofnanostructures is less than approximately 400 nanometers.

In one example of the lens, each nanostructure of the plurality ofnanostructures has a height that is less than or equal to the depth ofthe phase-adjusting region. The phase-adjusting region may be, forexample, a circular region or an annular region. In one example, lensfurther comprises at least one additional phase-adjusting region, and atleast one corresponding additional plurality of nanostructures formed inthe at least one additional phase-adjusting region. In one example, thenanostructures are uniformly spaced apart from one another. In anotherexample, the spacing between the adjacent nanostructures decreases froma largest spacing at a center of the phase-adjusting region to smallestspacing at edges of the phase-adjusting region. In another example, thespacing between the adjacent nanostructures is sufficiently small so asto prevent water from penetrating between the nanostructures atatmospheric pressure. A density of the plurality of nanostructures andthe depth of the phase-adjusting region may be selected based at leastin part on a predetermined desired average refractive index of thephase-adjusting region. The lens may be an ophthalmic contact lens, orany of numerous other types of optical lenses, as discussed above.

According to another embodiment, an imaging apparatus comprises a lensand a phase-adjusting optical element associated with the lens andconfigured to extend a depth of field of the lens, the phase-adjustingoptical element comprising a plurality of nanostructures, wherein aspacing between adjacent nanostructures of the plurality ofnanostructures is less than approximately 400 nanometers. The imagingapparatus may further comprises a detector optically coupled to the lensand configured to detect light passing through the lens, and a processorcoupled to the detector and configured to produce an image from thelight detected by the detector. The imaging apparatus may be, forexample, a camera.

In one example of the imaging apparatus, the phase-adjusting opticalelement comprises a surface relief on the lens including at least onefirst region and at least one second region, the at least one firstregion being recessed relative to the at least one second region,wherein the plurality of nanostructures are formed in the at least onefirst region and extend away from a base of the at least one firstregion. Each nanostructure of the plurality of nanostructures has aheight that may be less than or equal to a depth of the at least onefirst region. In one example, a density of the plurality ofnanostructures and a depth of the at least one first region are selectedbased at least in part on a predetermined desired average refractiveindex of the first region. In another example, the phase-adjustingoptical element comprises a surface relief on the lens defining aplurality of recessed regions, and a corresponding plurality of groupsof nanostructures, each group of nanostructures formed in a respectiveone of the plurality of recessed regions. The recessed regions may haveany of numerous different geometric or non-geometric shapes. In oneexample, the plurality of recessed regions comprises a plurality ofconcentric annular regions. In another example, the phase-adjustingoptical element comprises a surface relief on the lens defining eitheran annular region or a circular region, wherein the plurality ofnanostructures are formed in the annular or circular region and extendaway from a base of the annular or circular region.

Another embodiment is directed to a method of extending a depth of fieldof a lens, the method comprising forming a phase-adjusting region in asurface of the lens, the phase-adjusting region extending into the lensby a predetermined depth, and forming a plurality of nanostructures inthe phase-adjusting region, the plurality of nanostructures having adensity selected to provide a predetermined average index of refractionfor the phase-adjusting region.

In one example of the method, forming the phase-adjusting region andforming the plurality of nanostructures include etching the surface ofthe lens in the phase-adjusting region, and forming the phase-adjustingregion and forming the plurality of nanostructures are performedsimultaneously. The method may further comprise masking the surface ofthe lens with a pattern of the plurality of nanostructures prior toetching the surface of the lens. In one example, forming the pluralityof nanostructures includes forming a uniformly spaced plurality ofnanostructures. In another example, forming the plurality ofnanostructures includes forming a non-uniformly spaced plurality ofnanostructures. Forming the phase-adjusting region may include formingone of a circular region and an annular region in the surface of thelens.

Still other aspects, embodiments, and advantages of these exemplaryaspects and embodiments, are discussed in detail below. Any embodimentdisclosed herein may be combined with any other embodiment in any mannerconsistent with at least one of the objects, aims, and needs disclosedherein, and references to “an embodiment,” “some embodiments,” “analternate embodiment,” “various embodiments,” “one embodiment” or thelike are not necessarily mutually exclusive and are intended to indicatethat a particular feature, structure, or characteristic described inconnection with the embodiment may be included in at least oneembodiment. The appearances of such terms herein are not necessarily allreferring to the same embodiment. The accompanying drawings are includedto provide illustration and a further understanding of the variousaspects and embodiments, and are incorporated in and constitute a partof this specification. The drawings, together with the remainder of thespecification, serve to explain principles and operations of thedescribed and claimed aspects and embodiments

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

Various aspects of at least one embodiment are discussed below withreference to the accompanying figures, which are not intended to bedrawn to scale. Where technical features in the figures, detaileddescription or any claim are followed by references signs, the referencesigns have been included for the sole purpose of increasing theintelligibility of the figures, detailed description, and claims.Accordingly, neither the reference signs nor their absence are intendedto have any limiting effect on the scope of any claim elements. In thefigures, each identical or nearly identical component that isillustrated in various figures is represented by a like numeral. Forpurposes of clarity, not every component may be labeled in every figure.The figures are provided for the purposes of illustration andexplanation and are not intended as a definition of the limits of theinvention. In the figures:

FIG. 1 is a block diagram of one example of an imaging apparatusaccording to aspects of the invention;

FIG. 2A is a diagram of one example of a lens including aphase-adjusting element according to aspects of the invention;

FIG. 2B is a diagram of another example of a lens including aphase-adjusting element according to aspects of the invention;

FIG. 3A is a schematic plan view of the lens of FIG. 2A;

FIG. 3B is a schematic plan view of the lens of FIG. 2B;

FIG. 4 is a diagram of a simulated reference phase-adjusting element;

FIG. 5 is a diagram of the phase distribution of the perpendicularelectric field along the simulated reference element of FIG. 4;

FIG. 6A is a diagram of a simulated example of a phase-adjusting elementincluding an array of nanostructures according to aspects of theinvention;

FIG. 6B is an enlarged view of the portion of FIG. 6A contained in box6B in FIG. 6A, illustrating the simulated nanostructures according toaspects of the invention;

FIG. 7 is a diagram of the phase distribution of the perpendicularelectric field along the simulated phase-adjusting element of FIG. 6A;

FIG. 8A is a diagram of a cross section of the phase along the directionof light propagation in the simulated phase-adjusting element of FIG. 6Afor a nanostructure period of 300 nanometers and a nanostructure spacingof 200 nanometers; and

FIG. 8B is a diagram of a cross section of the phase along the directionof light propagation in the simulated phase-adjusting element of FIG. 6Afor a nanostructure period of 350 nanometers and a nanostructure spacingof 250 nanometers.

DETAILED DESCRIPTION

As discussed above, several technologies for extending the depth offield of a lens implement a phase-adjusting element to reshape the phaseof the optical signal passing though the lens, thereby achieving anextended depth of field. To maintain accurate phase reshaping, therefractive index difference between the phase-adjusting element and itssurroundings must be controlled with high precision. In liquidenvironments, however, the presence of the liquid in the phase-adjustingelement can significantly alter the refractive index of the element. Forexample, in ophthalmic applications the variable presence of tears inthe eyes can create a large uncertainty with respect to the refractiveindex of the space surrounding the phase-adjusting element at any giventime. Aspects and embodiments are directed to a phase-adjusting elementhaving a structure that provides liquid-invariant performance of thephase-adjusting element. In one embodiment, the phase-adjusting elementincludes at least one region having an array of nanostructures formedtherein. The region(s) produce a phase retardation in the longitudinalaxis of the lens (i.e. along an optical axis of the lens) to achieveextended depth of field for the lens, and the nanostructures inhibitmicro fluidic movement within the phase-adjusting element to provideliquid-invariant phase reshaping, as discussed further below.

It is to be appreciated that embodiments of the methods and apparatusesdiscussed herein are not limited in application to the details ofconstruction and the arrangement of components set forth in thefollowing description or illustrated in the accompanying drawings. Themethods and apparatuses are capable of implementation in otherembodiments and of being practiced or of being carried out in variousways. Examples of specific implementations are provided herein forillustrative purposes only and are not intended to be limiting. Inparticular, acts, elements and features discussed in connection with anyone or more embodiments are not intended to be excluded from a similarrole in any other embodiments.

Also, the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. Any references toembodiments or elements or acts of the systems and methods hereinreferred to in the singular may also embrace embodiments including aplurality of these elements, and any references in plural to anyembodiment or element or act herein may also embrace embodimentsincluding only a single element. References in the singular or pluralform are not intended to limit the presently disclosed systems ormethods, their components, acts, or elements. The use herein of“including,” “comprising,” “having,” “containing,” “involving,” andvariations thereof is meant to encompass the items listed thereafter andequivalents thereof as well as additional items. References to “or” maybe construed as inclusive so that any terms described using “or” mayindicate any of a single, more than one, and all of the described terms.Any references to front and back, left and right, top and bottom, upperand lower, and vertical and horizontal are intended for convenience ofdescription, not to limit the present systems and methods or theircomponents to any one positional or spatial orientation.

Referring to FIG. 1, there is illustrated a block diagram of an imagingapparatus 100 according to one embodiment which is configured to imagean object 110. The imaging apparatus 100 includes a lens 120, aphase-adjusting element 130, and a detector 140, and may also include aprocessor 160 configured to process images from the light detected bythe detector 140. The phase-adjusting element 130 is configured toprovide liquid-invariant extended depth of field for the lens 120, asdiscussed further below. The phase-adjusting element 130 may be aseparate element attached to the lens 120 or located close thereto, ormay be implemented integral with the lens 120, for example as a surfacerelief on the lens as discussed further below. For example, thephase-adjusting element 130 may include a pattern of spaced apart,optically transparent regions 150 that have a different refractive indexand/or different thickness compared to other regions of phase-adjustingelement and/or lens and thus affect the phase of the light passingtherethrough. The phase differences caused by the region(s) 150 aresmall, for example, less than π. In order to extend the depth of fieldof the lens 120, the phase differences caused by the region(s) 150 aredesigned to create a constructive/destructive interference pattern ofthe light passing through the phase-adjusting element. If a liquidenters the region(s) 150, the refractive index of the region willchange, and therefore the phase difference will change as well,resulting in a change in the interference pattern caused by thephase-adjusting element 130. To avoid this situation, according to oneembodiment, the region(s) 150 of the phase-adjusting element 130 are“roughened” to prevent liquid from entering the region(s); therebyimproving the robustness of the extended depth of field of the lens 120in environments where liquid may be present.

The imaging apparatus 100 may be used in a wide variety of equipment andapplications, such as, for example, cameras, machine visionapplications, photography, television systems, video conference systems,radar imaging systems, endoscopy and passive bio-medical inspections,tomography, display panels, etc. Embodiments of the imaging apparatusmay also be used in ophthalmic applications, such as a contact lens, aspectacle lens, an intraocular lens, or any other lens used around orinserted into any part of the eye. In these applications, the detector140 may be the retina and the processor 160 may include part of thebrain.

As discussed above, according to one embodiment, the phase-adjustingelement 130 is implemented integral with the lens 120. Accordingly,referring to FIG. 2A, there is illustrated a diagram of a lens 200including a phase-adjusting element according to one embodiment. Thelens 200 has a surface 210 which has a modulated relief therebycomprising a plurality of regions including a first region 220 and asecond region 230. The first region 220 being recessed and having adepth 240 relative to the second region 230. A plurality ofnanostructures 260 are formed in the first region 220, extending upwardfrom the base of the first region, as illustrated in FIG. 2A. Thephase-adjusting element 130 comprises the combination of the modulatedlens surface 210 and the plurality of nanostructures 260. As usedherein, the term “nanostructure” is intended to refer to a structure ofintermediate size between molecular and microscopic (micrometer-sized),and which is small relative to the size of the overall object in whichit is formed. The term “nanostructure” as used herein does not requirethe structure to be smaller than 100 nanometers in a given dimension.

Referring to FIG. 2A, the first region 220 has a lateral width 250 thatis at least one wavelength at the lower (red) end of the visiblespectrum. In one example, the lateral width 250 of the first region islarge compared to the wavelengths of visible light, for example, atleast several wavelengths at the lower end of the visible spectrum.Thus, the surface relief of the lens 200 does not cause diffraction ofvisible light passing through the phase-adjusting element because thesurface relief is laterally large compared to the wavelengths of visiblelight. The nanostructures 260 each have a lateral width 270 and arespaced apart from one another by a spacing 280. This spacing 280 may bemade small such that the light wave is substantially unaffected otherthan to see change in the average index of refraction of the firstregion. The spacing 280 may be selected based on at least the followingfactors. First, the spacing 280 is less than approximately onewavelength at the higher (blue) end of the visible light spectrum toavoid scattering diffraction and prevent generation of undesireddiffraction orders. Second, as discussed further below, the density ofthe nanostructures (determined by the spacing 280) and the depth 240 ofthe first region 220 are selected to provide a desired average index ofrefraction for the first region. In addition, the spacing 280 isselected to prevent micro fluidic movement in the first region 220, asalso discussed further below. The height of the nanostructures 260 maybe up to approximately the depth 240. In one embodiment, the depth 240of the first region 220 is small, for example, less than the opticalwavelength.

According to one embodiment, the array of nanostructures 260 forms abinary grating that has an average index of refraction. Because thespacing 280 between the nanostructures 260 is smaller than the opticalwavelength, the array of nanostructures does not diffract visible light;instead the light “sees” the first region 220 as a whole having anaverage index of refraction, determined by the material of thenanostructures and the interstitial substance (e.g., the surroundingliquid or air), rather than an array of distinct nanostructures. As aresult, the phase-adjusting element is not diffractive to visible lightpassing therethrough; instead substantially all the light remains in thezeroth order. Accordingly, the phase-adjusting element may be termed“non-diffractive” to visible light. In one embodiment, thephase-adjusting element is also not refractive in that it does notprovide optical power. It is to be appreciated that although in oneembodiment the phase-adjusting element is not refractive, the associatedoptical lens 200 may be refractive. As used herein, the term“non-diffractive” is intended to mean a structure that may be notdiffractive (as described above) and also not refractive (as describedabove).

The phase-adjusting element 130 may be formed using any of a variety oftechniques, depending for example on the material of the lens 200 andwhether or not the phase-adjusting element 130 is integral with the lensor a separate element. For example, the phase-adjusting element may beformed by selectively etching the lens surface 210 to create themodulated relief and array of nanostructures. In this example, thenanostructures 260 may be formed simultaneously with the pattern of thesurface relief, and are made of the same material as the lens itself.The etching process may be a chemical etching process or a mechanicaletching process. In another example, the nanostructures may be formedusing a deposition process to deposit or “grow” the nanostructures onthe surface 210 of the lens 200, in which case the nanostructures maycomprise the same material as the lens or a different material.

In the example illustrated in FIG. 2A, the first region 220 is anapproximately circular region formed in the surface of the lens 200, asillustrated in FIG. 3B. However, it is to be appreciated that the firstregion 220 may assume numerous shapes, not limited to the exampleillustrated in FIGS. 2A and 3A. For example, referring to FIG. 2B thereis illustrated another example of a lens 200 in which the first region220 is an annular region (as illustrated in FIG. 3B). The first region220 may also assume numerous other shapes, such as, but not limited to,rectangular, square, and other geometric or non-geometric shapes of thesame lateral width or different lateral widths. In addition, althoughFIG. 2A illustrates a single first region 220, the phase-adjustingelement may include multiple first regions 220, and multiple secondregions 230, and is not limited to a single first region or singlesecond region. For example, the first region 220 may comprise a seriesof concentric annular regions, optionally including a centralsubstantially circular region, with a second region 230 disposed betweeneach adjacent pair of concentric first regions. In addition, the shapeof the first region 220 may vary depending on the shape of the lens 200.Furthermore, the shape of the nanostructures is not limited to thetriangular shape illustrated in FIGS. 2A and 2B. The nanostructures mayhave any of a variety of shapes, which may depend (at least in part) onthe manufacturing process used to form the nanostructures, and which mayinclude, for example, rectangular, dome, cylindrical or random shapes.

The phase retardation caused by the first region 220 depends on theaverage index of refraction of the region, which is determined by thedepth 240 and the density of the nanostructures 260. The depth 240 canbe calculated according to the following equation:

$\begin{matrix}{\delta = \frac{{\Delta\varphi}_{d}\lambda_{0}}{2{\pi \left( {n - n_{eff}} \right)}}} & (1)\end{matrix}$

In equation (1), δ is the depth 240, λ₀ is the nominal wavelength of thelight, n is the refractive index of the lens, n_(eff) is the averagerefractive index of the first region 220, given by equation (2) below,and Δφd is the desired phase retardation that the first region 220 isconfigured to provide.

$\begin{matrix}{n_{eff} = \frac{{\Delta \; {x \cdot M \cdot n}} + \left( {L - {\Delta \; {x \cdot M}}} \right)}{L}} & (2)\end{matrix}$

In equation (2), Δx is the average width 270 of the nanostructures 260,M is the number of nanostructures in the first region 220, and L is thelateral width 250 of the first region 220. Accordingly, the depth 240 ofthe first region 220 can be calculated based on a known desired phaseretardation and a known average index of refraction of the first region,and the average index of refraction can be determined based on a knownlateral width 250 of the first region and the size and density of thenanostructures 260 within the first region.

Any of the above-mentioned parameters may be varied, subject to certainconstraints (such as, for example, manufacturing capability, andsuitable materials for the lens, optical constraints, etc.) to achieve astructure for the phase-adjusting element that achieves a desired phaseretardation and therefore a desired interference pattern to extend thedepth of field of the lens 200. One optical constraint is the density ofthe nanostructures 260. In particular, the spacing 280 between thenanostructures 260 may be less than approximately the nominal opticalwavelength λ₀ to avoid generating undesired diffraction orders. In oneexample, the spacing 280 between the nanostructures 260 is less than 400nanometers (nm), for example, in a range of approximately 300 nm to 400nm. The spacing 280 may be made smaller than the shortest wavelength inthe visible spectrum such that the phase-adjusting element isnon-diffractive to visible light. The nanostructures 260 may be madenearly adjacent, particularly as advances in modern chemical processingtechniques have made it possible to achieve a very dense structure withgood repeatability; however, as the density of the nanostructures in thefirst region 220 increases, the average refractive index of the firstregion also increases. Therefore, to maintain a given average refractiveindex, for a denser array of nanostructures 260, the depth 240 of thefirst region 220 may be increased, according to equations (1) and (2)given above. In one example, a depth 240 of approximately 1 micrometer(μm) to approximately 1.5 μm is presently practical for ophthalmiccontact lenses.

According to one embodiment, the nanostructures 260 are sufficientlyclosely spaced to create a surface tension that is greater than thepressure of the liquid; hence the array of nanostructures will maintaina steady state environment within the first region 220 even in thepresence of the liquid. For example, for ophthalmic contact lenses, thenanostructures may be sufficiently closely spaced to prevent tears fromentering the first region 220 at approximately atmospheric pressure(experienced at or near the Earth's surface). The lens 200 including thephase-adjusting element can be configured to account for two steadystate conditions in which micro fluidics movement inside the firstregion 220 is substantially prevented. In the first configuration, thearray of nanostructures 260 prevents liquids from penetrating the firstregion 220 between the nanostructures in a hydrophobic material. In thesecond configuration, the nanostructure 260 are either made from ahydrophilic material or such a material is provided in the space betweenthe nanostructures 260 of the first region 220 such that the spacebetween these nanostructures is constantly filled with the surroundingliquid. The configuration of the lens 200 may be selected based on anexpected environment in which the lens is to be used. For example, inenvironments where liquid is only sporadically present, the firstconfiguration may be preferred. The following simulations, whichdemonstrate performance of an example of the lens 200 including anembodiment of the phase-adjusting element, assume a hydrophilic materialand therefore demonstrate performance of the structure for the moresevere diffraction case since the wavelength of the light is shorter dueto the presence of the liquid.

An example of the phase-adjusting element 130 including a nanostructurearray was simulated using Comsol Multiphysics, a modeling and simulationprogram available from the COMSOL Group, to solve Maxwell's waveequation via the finite element method. A reference phase-adjustingelement, including recessed region without any nanostructure array, wasalso simulated to provide reference data with which to compare thesimulation results obtained for the example phase-adjusting element 130.For both simulations, the illumination was a normally incident TEpolarized plane wave having a wavelength λ₀ of 550 nm in free space.

A diagram of the simulated reference element 400 is illustrated in FIG.4. The reference element has a recessed region 410, corresponding to thefirst region 220 of lens 200 in FIG. 2A, formed in a surroundingmaterial 420. The recessed region 410 has a width 440 of 300 μm and adepth 430 (δ) that matches the π condition of equation (3):

$\begin{matrix}{\delta = \frac{\lambda_{0}}{2\Delta \; n}} & (3)\end{matrix}$

In equation (3), Δn is the difference between the refractive index ofthe surrounding material 420 and the refractive index of the environment450. For the simulations, the surrounding material is specified as BK7optical glass having a refractive index of 1.517, and the environment450 is specified as water having a refractive index of 1.3. Accordingly,from equation (3), the recessed region had a depth δ=1.267 μm. The totalwidth of the simulated structure is 0.8 millimeters (mm) and the length(in the dimension of the depth 450) is 3.5 μm.

Referring to FIG. 5 there is illustrated the simulated phasedistribution of the perpendicular electric field along the referenceelement 400 of FIG. 4. FIG. 5 demonstrates that the phase differencebetween the recessed region 410 and the surrounding material 420 islinearly summed along depth the recessed region 410 with a phase delayof π generated at the end of the 1.267 μm recessed region. Thus, thereference element 400 implements an inverting phase plate.

Referring to FIG. 6A there is illustrated a diagram of a simulatedexample of a phase-adjusting element 600 including a nanostructure arrayformed in a first region 610 corresponding to the first region 220 inFIG. 2A. Surrounding the first region 610 is the second region 620,corresponding to the second region 230 in FIG. 2A. FIG. 6B is anenlarged view of the portion of the phase-adjusting element 600 enclosedin box 6B in FIG. 6A, illustrating the nanostructures 630 formed in thefirst region 610. In the simulated example, 1000 nanostructures 630 aredefined in the first region 610 and the nanostructures 630 are uniformlyspaced (i.e., arranged in a regular pattern across the width 440 of thefirst region 610) with period of 300 nm and a duty cycle of 33.3% (i.e.,each nanostructure is 100 nm wide and the spacing between adjacentnanostructures is 200 nm). The width 440 of the first region 610 is 300μm, the same as the width 440 of the reference element. The material ofthe second region 620 is specified as BK7 with a refractive index of1.517. As can be seen in FIG. 6B, and as discussed above, for thesimulation, the water 450 entirely fills the space between thenanostructures 630 in the first region 610. Thus, the average refractiveindex for the first region can be calculated based on the refractiveindexes of the BK7 (from which the nanostructures are made) and thewater, and the duty cycle. From equation (3), to maintain the same phaseshift of π as generated by the reference element, the depth 640 of thefirst region 610 is made to be 1.9 μm.

Reference is now made to FIG. 7 illustrating the phase distribution ofthe perpendicular electric field along the simulated phase-adjustingelement 600. As can be seen with reference to FIG. 7, the phase of theelectric field of the light in the first region 610 accumulates a linearphase shift along the depth of the first region 610 and maintains aplane wave phase front in both the first region 610 and the secondregion 620. The phase along the end of the first region 610 shows aphase difference of nearly π and the propagating field maintains thephase difference until the end of the simulated phase-adjusting element600. Thus, the phase-adjusting element with the nanostructures 630realizes an inverting phase shifter that produces a plane wave frontwith no diffraction caused by the nanostructures.

Cross sections of the phase along the direction of light propagation areillustrated in FIGS. 8A and 8B. FIG. 8A illustrates the phase for thephase-adjusting element 610 discussed above having a spacing of 200 nmbetween the nanostructures. As can be seen with reference to FIG. 8A,the phase delay in the first region 610 shows a constant phase along thefirst region and the phase delay is linear with the light propagationinside the first region 610. FIG. 8B illustrates the phase for anexample of the phase-adjusting element 610 with the nanostructure arrayhaving a period of 350 nm and a duty cycle of 28%. Thus, in the exampleof FIG. 8B, each nanostructure 630 is 100 nm wide and the spacingbetween adjacent nanostructures is 250 nm. The other dimensions andcharacteristics of the phase-adjusting element 610 are the same asdiscussed above. This increased spacing approaches the wavelength of thelight in BK7. As can be seen with reference to FIG. 8B, the ripple inthe phase implies a minor diffraction pattern caused by the largerspacing between the nanostructures 630. Accordingly, in order to avoidany type of diffraction, the spacing between the nanostructures may bekept under approximately a half wavelength (in free space) to accountfor the shortening of the wavelength of the light as it passes throughthe material of phase-adjusting element.

Referring again to FIG. 7, the visible distortion 710 in the phase atthe edge of the first region 610 is caused by the sharp transitionbetween the first region 610 which contains the nanostructures and thesecond region 620 due the difference in the refractive index between thetwo regions. This distortion may be reduced by “softening” thetransition between the first region and the second region, for example,by implementing a graded change in the refractive index. In oneembodiment, the spacing 280 between the nanostructures 260 is madevariable with a largest spacing (and therefore lowest refractive index)toward a center of the first region 220 and a smallest spacing (andtherefore highest refractive index, closest to the refractive index ofthe second region 230) toward the edges of the first region. Byimplementing a slowly increasing spacing 280 from the edges of the firstregion to the center of the first region, the average refractive indexof the first region can be made to transition more gradually from thatof the second region, reducing any edge distortion in the phase. It isto be appreciated that many variations in the spacing 280 between thenanostructures can be implemented. For example, the spacing 280 may beuniform, may increase from the edges of the first region 220 towards thecenter of the first region, may be “stepped” (i.e., groups ofnanostructures may each have a specified spacing which may differ fromgroup to group), may vary differently along different axes of thephase-adjusting element, or may be random.

According to one embodiment, the phase-adjusting element issubstantially purely phase-affecting such that it alters the phase ofthe light passing therethrough, but does not substantially affect theamplitude of the light. In one example, the “surface roughness” due tothe nanostructures 260 causes a scattering effect which causes a smallamplitude change in the light. In other examples, however, thephase-adjusting element is configured to cause a substantial andcontrolled change in the amplitude of the light as well as the phase.

Having thus described several aspects of at least one embodiment, it isto be appreciated various alterations, modifications, and improvementswill readily occur to those skilled in the art. Such alterations,modifications, and improvements are intended to be part of thisdisclosure and are intended to be within the scope of the invention.Accordingly, the foregoing description and drawings are by way ofexample only, and the scope of the invention should be determined fromproper construction of the appended claims, and their equivalents.

1-38. (canceled)
 39. A lens comprising a surface having a surface reliefcomprising a plurality of regions including at least one pair of firstand second adjacent regions, the first and second regions beingconfigured to differently affect phase of light passing through saidregions to thereby induce a desired phase difference and provide desiredextension of a depth of field of the lens, wherein one of the first andsecond regions has a pattern providing surface roughness in said regionsuch as to prevent liquid from entering said region thereby maintainingsaid phase difference for light passing through the first and secondregions.
 40. The lens as claimed in claim 39, wherein spacing betweenfeatures of said pattern is sufficiently small to prevent liquid frompenetrating between the features.
 41. The lens as claimed in claim 39,wherein the first region, being the region having said pattern definingthe surface roughness, has a depth relative to the second region. 42.The lens as claimed in claim 41, wherein the first region has certainaverage refractive index defined by said depth of the first region anddensity of features of said pattern within the first region.
 43. Thelens as claimed in claim 42, wherein said pattern is in the form of anarray of nanostructures extending away from the base of said region. 44.The lens as claimed in claim 41, wherein a lateral width of the firstregion is large compared to wavelengths of visible light, such that thesurface relief does not cause diffraction of light of the visible range.45. The lens as claimed in claim 43, wherein spacing between thefeatures of the pattern is less than approximately a shortest wavelengthof visible light in free space.
 46. The lens as claimed in claim 43,wherein the nanostructures are of a height that is less than or equal tothe depth of the first region.
 47. The lens as claimed in claim 39,wherein the first region has one of the following configurations: thefirst region is a circular region, the first region is an annularregion, and the first region comprises a plurality of concentric zones.48. The lens as claimed in claim 40, wherein the pattern has one of thefollowing arrangements of features: the features are equally spaced, orspacing between adjacent features decreases from a largest spacing at acenter of the first region to smallest spacing at edges of the firstregion.
 49. The lens as claimed in claim 43, wherein the nanostructuresare either uniformly spaced apart from one another, or are arranged withvarying spacing between them such that spacing adjacent nanostructuresdecreases from a largest spacing at a center of the first region tosmallest spacing at edges of the first region.
 50. The lens as claimedin claim 39, wherein the lens is an ophthalmic contact lens.
 51. Thelens as claimed in claim 50, wherein said pattern is in the form of anarray of nanostructures extending away from the base of the firstregion, spacing between the adjacent nanostructures being sufficientlysmall to prevent liquid from penetrating between the nanostructures atatmospheric pressure; the first region having a depth relative to thesecond region, the certain average refractive index of the first regionbeing defined by said depth of the first region and by density of thenanostructures within the first region.
 52. A lens having a depth offield, the lens comprising: a phase-adjusting region formed in a lenssurface of the lens, the phase-adjusting region extending into the lensby a depth and configured to extend the depth of field of the lens; anda plurality of nanostructures formed in the phase-adjusting region, theplurality of nanostructures extending away from a base of thephase-adjusting region.
 53. The lens as claimed in claim 52, wherein thenanostructures are of a height that is less than or equal to the depthof the phase-adjusting region.
 54. The lens as claimed in claim 52,wherein the phase-adjusting region comprises one or more a circular orannular regions.
 55. The lens as claimed in claim 52, furthercomprising: at least one additional phase-adjusting region; and at leastone corresponding additional plurality of nanostructures formed in theat least one additional phase-adjusting region.
 56. The lens as claimedin claim 52, wherein the nanostructures are either uniformly spacedapart from one another, or the spacing between the adjacentnanostructures decreases from a largest spacing at a center of thephase-adjusting region to smallest spacing at edges of thephase-adjusting region.
 57. The lens as claimed in claim 52, wherein adensity of the plurality of nanostructures and the depth of thephase-adjusting region are selected based at least in part on apredetermined desired average refractive index of the phase-adjustingregion.
 58. The lens as claimed in claim 52, wherein the lens is anophthalmic contact lens with the extended depth of field, where theplurality of nanostructures prevent liquid from entering thephase-adjusting region.
 59. The lens as claimed in claim 52, wherein alateral width of the phase-adjusting region is large compared towavelengths of visible light, such as not to cause diffraction of lightof the visible range.
 60. An imaging apparatus comprising: a lens; and aphase-adjusting optical element associated with the lens and configuredto extend a depth of field of the lens, the phase-adjusting opticalelement comprising a surface relief on the lens surface including atleast one first region and at least one second region, the at least onefirst region being recessed relative to the at least one second regionand comprising a plurality of nanostructures extending away from a baseof said first region.
 61. The imaging apparatus as claimed in claim 60,further comprising: a detector optically coupled to the lens andconfigured to detect light passing through the lens; and a processorcoupled to the detector and configured to produce an image from thelight detected by the detector.
 62. The imaging apparatus as claimed inclaim 60, wherein the nanostructures are of a height that is less thanor equal to a depth of the at least one first region.
 63. The imagingapparatus as claimed in claim 60, wherein a density of the plurality ofnanostructures and a depth of the at least one first region are selectedbased at least in part on a predetermined desired average refractiveindex of the at least one first region.
 64. The imaging apparatus asclaimed in claim 60, wherein: said surface relief on the lens defines aplurality of the recessed regions; and a corresponding plurality ofgroups of the nanostructures, each group of the nanostructures formed ina respective one of the plurality of recessed regions.
 65. The imagingapparatus as claimed in claim 64, wherein the plurality of recessedregions comprises a plurality of concentric annular regions.